报告题目：Scaled Proximal Gradient Methods for Sparse Optimization Problems
报告时间：2024年9月27月（周五）下午3：30-4：30
报告地址：广东技术师范大学工业中心605
报告人：白正简教授
报告人简介：
白正简，厦门大学教授、博士生导师，教育部新世纪优秀人才支持计划入选者、福建省杰出青年基金获得者。2004年博士毕业于香港中文大学，曾在新加坡国立大学和意大利Insubria大学作博士后和访问学者。主要研究方向为数值代数、特征值问题及其逆问题、稀疏优化、矩阵流形上的优化算法及其在数据科学中的应用等。曾主持国家自然科学基金面上项目和福建省自然科学基金项目。在SIAM J. Matrix Anal. Appl., SIAM J. Numer. Anal., Numer. Math., Inverse Problems, J. Sci. Comput.等本学科主流期刊上发表学术论文40余篇。曾获得福建省科学技术奖二等奖。
报告提要：
The sinc-Nyström method is a high-order numerical method in time for evolutionary differential equations. But it has to solve all the time steps in one shot (i.e., all-at-once), which results in a large-scale structured nonsymmetric dense linear system. In this talk, we introduce parallel-in-time preconditioners for such dense linear systems. The proposed preconditioner is a low-rank perturbation of the original matrix, and it has twoadvantages. First, the eigenvalues of the preconditioned system are highly clustered with some uniform bounds which are independent of the mesh parameters. Second, the preconditioner can be computed in parallel-in-time via diagonalization technique. The effectiveness of our proposed preconditioners is illustrated by several numerical examples.
报告题目：Randomized tensor wheel decomposition
报告时间：2024年9月27月（周五）下午4：30-5：30
报告地址：广东技术师范大学工业中心605
报告人：李寒宇教授
报告人简介：
李寒宇，博士、重庆大学教授、博士生导师，中国数学会计算数学分会理事、重庆市工业与应用数学学会副理事长。主要从事随机数值代数、张量计算等方面的研究。先后主持国家自然科学基金项目、重庆市自然科学基金项目多项，在SISC、SIMAX、NLA、BIT等国际知名期刊发表学术论文40多篇。
内容提要：
Tensor wheel (TW) decomposition is an elegant compromise of the popular tensor ring decomposition and fully-connected tensor network decomposition, and has many applications. In this work, we investigate the computation of this decomposition. Three randomized algorithms based on random sampling or random projection are proposed. Specifically, by defining a new tensor product called subwheel product, the structures of the coefficient matrices of the alternating least squares subproblems from the minimization problem of TW decomposition are first figured out. Then, using the structures and the properties of subwheel product, a random sampling algorithm based on leverage sampling and two random projection algorithms respectively based on Kronecker sub-sampled randomized Fourier transform and TensorSketch are derived. These algorithms can implement the sampling and projection on TW factors and hence can avoid forming the full coefficient matrices of subproblems. We present the complexity analysis and numerical performance on synthetic data, real data, and image reconstruction for our algorithms. Experimental results show that, compared with the deterministic algorithm in the literature, they need much less computing time while achieving similar accuracy and reconstruction effect. We also apply the proposed algorithms to tensor completion and find that the sampling-based algorithm always has excellent performance and the projection-based algorithms behave well when the sampling rate is higher than 50%.
报告题目：Nonnegative Low Multi-Rank Third-order Tensor Approximation via Transformation
报告时间：2024年9月27日（周五）下午5：30-6：30
报告地址：广东技术师范大学工业中心605
报告人：宋广景教授
报告人简介：
宋广景教授，香港浸会大学博士后，新加坡国立大学高级访问学者，山东科技大学博士生导师，中国高等教育学会教育数学专业委员会常务理事、Symmetry等SCI期刊编委。主要从事矩阵、张量分析及其应用研究，博士论文获上海市研究生优秀成果奖，近五年以第一作者或通信作者在《Numerische Mathematik》、《SIAM Journal On Matrix Analysis and Applications》、《Applied and Computational Harmonic Analysis》、《IEEE Transactions on Knowledge and Data Engineering》等国际权威期刊上发表论文20余篇，其中高被引论文1篇，SCI他引600余次。主持完成国家自然科学基金、山东省自然科学基金重点项目、中国博士后基金、山东省自然科学基金和山东省高校科技发展计划各一项，现主持在研国家自然科学基金面上项目一项。
报告提要：
The sinc-Nyström method is a high-order numerical method in time for evolutionary differential equations. But it has to solve all the time steps in one shot (i.e., all-at-once), which results in a large-scale structured nonsymmetric dense linear system. In this talk, we introduce parallel-in-time preconditioners for such dense linear systems. The proposed preconditioner is a low-rank perturbation of the original matrix, and it has twoadvantages. First, the eigenvalues of the preconditioned system are highly clustered with some uniform bounds which are independent of the mesh parameters. Second, the preconditioner can be computed in parallel-in-time via diagonalization technique. The effectiveness of our proposed preconditioners is illustrated by several numerical examples.
报告题目：Generalized Tensor Function via the Tensor Singular Value Decomposition based on the Tensor-Tensor Decomposition
报告时间：2024年9月29日（周日）上午9：00-10：00
报告地址：广东技术师范大学工业中心803
报告人：魏益民教授
报告人简介：
魏益民，复旦大学数学科学学院教授、博士生导师，主要从事矩阵/张量方面的理论和应用研究，多次主持国家自然科学基金面上项目、教育部博士点基金项目和973子课题等项目。担任国际学术期刊Computational and Applied Mathematics, Journal of Applied Mathematics and Computing，FILOMAT,Communications in Mathematical Research,《高校计算数学学报》的编委.在国际学术期刊Math. Comput.,SIAM J. Sci. Comput.,SIAM J. Numer Anal., SIAM J. Matrix Anal. Appl.,J. Sci. Comput.,IEEE Trans. Auto. Control, IEEE Trans. Neural Network Learn. System，Neurocomputing和Neural Computation等发表论文150余篇；在EDP Science，Elsevier，Springer，World Scientific和科学出版社等出版英语专著5本, 5次入选爱思唯尔“中国高被引学者”榜单,Google学术引用8900余次，H指数48。
内容提要：
In this paper, we present the definition of generalized tensor function according to the tensor singular value decomposition (T-SVD) based on the tensor T-product. Also, we introduce the compact singular value decomposition (T-CSVD) of tensors, from which the projection operators and Moore-Penrose inverse of tensors are obtained. We establish the Cauchy integral formula for tensors by using the partial isometry tensors and apply it into the solution of tensor equations. Then we establish the generalized tensor power and the Taylor expansion of tensors. Explicit generalized tensor functions are listed. We define the tensor bilinear and sesquilinear forms and propose theorems on structures preserved by generalized tensor functions. For complex tensors, we established an isomorphism between complex tensors and real tensors. In the last part of our paper, we find that the block circulant operator establishes an isomorphism between tensors and matrices. This isomorphism is used to prove the F-stochastic structure is invariant under generalized tensor functions. The concept of invariant tensor cones is raised.
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计算机科学学院
2024年9月26日
